






import numpy as np
from PIL import Image





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			Optional[int]:

     '''simple docstring'''
     UpperCAmelCase__      :  int				      =			np.array(lowercase_       )
     if arr.shape[0] != arr.shape[1]:
          raise ValueError("""The input array is not a square matrix"""       )
     UpperCAmelCase__      :  Tuple				      =			0
     UpperCAmelCase__      :  Union[str, Any]				      =			0
     UpperCAmelCase__      :  Any				      =			0
     UpperCAmelCase__      :  Dict				      =			0

     # compute the shape of the output matrix
     UpperCAmelCase__      :  str				      =			(arr.shape[0] - size) // stride + 1
     # initialize the output matrix with zeros of shape maxpool_shape
     UpperCAmelCase__      :  Optional[int]				      =			np.zeros((maxpool_shape, maxpool_shape)       )

     while i < arr.shape[0]:
          if i + size > arr.shape[0]:
               # if the end of the matrix is reached, break
               break
          while j < arr.shape[1]:
               # if the end of the matrix is reached, break
               if j + size > arr.shape[1]:
                    break
               # compute the maximum of the pooling matrix
               UpperCAmelCase__      :  List[str]				      =			np.max(arr[i : i + size, j : j + size]       )
               # shift the pooling matrix by stride of column pixels
               j += stride
               mat_j += 1

          # shift the pooling matrix by stride of row pixels
          i += stride
          mat_i += 1

          # reset the column index to 0
          UpperCAmelCase__      :  List[Any]				      =			0
          UpperCAmelCase__      :  str				      =			0

     return updated_arr





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			Optional[Any]:

     '''simple docstring'''
     UpperCAmelCase__      :  List[str]				      =			np.array(lowercase_       )
     if arr.shape[0] != arr.shape[1]:
          raise ValueError("""The input array is not a square matrix"""       )
     UpperCAmelCase__      :  Optional[int]				      =			0
     UpperCAmelCase__      :  List[Any]				      =			0
     UpperCAmelCase__      :  Optional[Any]				      =			0
     UpperCAmelCase__      :  List[Any]				      =			0

     # compute the shape of the output matrix
     UpperCAmelCase__      :  str				      =			(arr.shape[0] - size) // stride + 1
     # initialize the output matrix with zeros of shape avgpool_shape
     UpperCAmelCase__      :  Union[str, Any]				      =			np.zeros((avgpool_shape, avgpool_shape)       )

     while i < arr.shape[0]:
          # if the end of the matrix is reached, break
          if i + size > arr.shape[0]:
               break
          while j < arr.shape[1]:
               # if the end of the matrix is reached, break
               if j + size > arr.shape[1]:
                    break
               # compute the average of the pooling matrix
               UpperCAmelCase__      :  Dict				      =			int(np.average(arr[i : i + size, j : j + size]       )       )
               # shift the pooling matrix by stride of column pixels
               j += stride
               mat_j += 1

          # shift the pooling matrix by stride of row pixels
          i += stride
          mat_i += 1
          # reset the column index to 0
          UpperCAmelCase__      :  Any				      =			0
          UpperCAmelCase__      :  List[Any]				      =			0

     return updated_arr


# Main Function
if __name__ == "__main__":
      from doctest import testmod

      testmod(name="""avgpooling""", verbose=True)

      # Loading the image
      SCREAMING_SNAKE_CASE__		:							Union[str, Any] 				=				Image.open("""path_to_image""")

      # Converting the image to numpy array and maxpooling, displaying the result
      # Ensure that the image is a square matrix

      Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

      # Converting the image to numpy array and averagepooling, displaying the result
      # Ensure that the image is a square matrix

      Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()














'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  int = 1_000_000   ):
       """simple docstring"""




       a_						     =			set(range(3   ,       lowercase_   ,       2   )   )
       primes.add(2   )
       for p in range(3   ,       lowercase_   ,       2   ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p   ,       lowercase_   ,       lowercase_   )   )   )

       a_						     =			[float(lowercase_   ) for n in range(limit + 1   )]

       for p in primes:
              for n in range(lowercase_   ,       limit + 1   ,       lowercase_   ):
                     phi[n] *= 1 - 1 / p

       return int(sum(phi[2:]   )   )


if __name__ == "__main__":
  print(f"""{solution() = }""")




